A method and apparatus is provided which allows a computer graphics system to accurately determine the actual depth value for pixels on a display screen which lie at the same depth as an associated surface. The associated surface is identified such that the delta z value with respect to the x and y direction along the surface can be calculated. The present invention then determines whether the line being considered is contained within a surface, or is an edge lying between, and adjacent to two surfaces. If the line is contained within a surface, the delta z value is initially added to the known endpoints of the line and then successively added, in the incremental x or y directions, to the pixels selected to represent the line. If the line is an edge, and includes selected pixels which lie on both associated surfaces, a filter is invoked that prevents those pixels corresponding to the surface, other than the surface first being considered, from being processed. The pixels being considered are then drawn in the same manner as a line within a surface. In this manner, the actual z value for each selected pixel can be determined and any hidden line, hidden surface removal problems are eliminated.